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A 25xx10^(-3)m^(3) volume cylinder is fi...

A `25xx10^(-3)m^(3)` volume cylinder is filled with 1 mol of `O_2` gas at room temperature (300 K).The molecular diameter of `O_2`, and its root mean square speed, are found to be 0.3 nm and `200 m//s`, respectively.What is the average collision rate (per second) for an `O_2` molecule ?

A

`~10^(11)`

B

`~10^(12)`

C

`~10^(10)`

D

`~10^(13)`

Text Solution

Verified by Experts

The correct Answer is:
C
Collision frequency `=pi d^(2)sqrt(2)V_("avg")(nN_(A))/V`
`V_("ang")`: Avg. speed
V: Volume of container
Putting values
Collision frequency `=3.14 xx (0.3 xx 10^(-9))^(2) xx sqrt(2) xx sqrt(8/(3pi)) xx V_("rms") xx (1 xx 6.023 xx 10^(23))/(25 xx 10^(-3))`
`1.8 xx 10^(9) ~~ 10^(10)` order.
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